Adding and subtracting mixed fractions
Suppose, you and your sister went to market.
There you both entered a cosmetic shop.
You asked shopkeeper to show some ribbons.
You buy
$234â€‹$
meter ribbon and your sister buys
$453â€‹$
meter ribbon.
Now, you ask shopkeeper the total length of the ribbon which you both bought.
And, after doing some calculation he told you that total length is
$71514â€‹$
meter.
Now, you are surprised to see that the shopkeeper can add these mixed fractions easily.
So, you ask your sister about this calculation.
And, your sister replied that first he convert mixed fractions into improper fractions and then, did the operation.
Letâ€™s understand how to add two mixed fractions.
Suppose, we have a problem to add these mixed fractions.
First, we convert these mixed fractions into improper fractions.
We convert these fractions into improper fractions as
We can add two fractions only if the denominators are same. So, letâ€™s try to make the denominator equal.
Letâ€™s take LCM of
$7$
and
$4$
which is
$28$
as
Now, make the denominators equal as
As the LCM is
$28$
, so we multiply
$31/7$
by
$4/4$
and
$26/4$
by
$7/7$
Now, add both the numerator and as the denominators are same as
Similarly, we can find the subtraction of mixed fractions by converting them into improper fractions.
Suppose, we consider an example and try to find the subtraction of these mixed fractions.
First we convert them into improper fraction as
Then, we take LCM of the denominators as
As the LCM is
$4$
, so we multiply
$17/4$
by
$1/1$
and
$7/2$
by
$2/2$
to make the denominator
$4$
.
Now, the denominator is same, we subtract
$10$
from
$17$
.
Revision
The another method is to convert them into improper fractions and then by taking LCM we can find the operation on the mixed fractions.
To add or subtract two mixed fractions, first convert these mixed fraction into improper fraction.
Take the LCM of the denominators and make the denominator equal.
As we make both denominators equal, we can add or subtract the numerators.
The End